First-order perturbation for multi-parameter center families
Itikawa, Jackson (Universidade Federal de Rondônia. Departament of Mathematics)
Oliveira, Regilene (Universidade de São Paulo. Departamento de Matemática)
Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2022
Abstract:	In the weak 16th Hilbert problem, the Poincaré-Pontryagin-Melnikov function, M(h), is used for obtaining isolated periodic orbits bifurcating from centers up to a first-order analysis. This problem becomes more difficult when a family of centers is considered. In this work we provide a compact expression for the first-order Taylor series of the function M(h,a) with respect to a, being a the multi-parameter in the unperturbed center family. More concretely, when the center family has an explicit first integral or inverse integrating factor depending on a. We use this new bifurcation mechanism to increase the number of limit cycles appearing up to a first-order analysis without the difficulties that higher-order studies present. We show its effectiveness by applying it to some classical examples.
Grants:	Agencia Estatal de Investigación PID2019-104658GB-I00 Ministerio de Ciencia e Innovación CEX2020-001084-M Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
Note:	Altres ajuts: acords transformatius de la UAB
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Limit cycle ; Melnikov functions ; Averaging theory ; Multi-parameter perturbation
Published in:	Journal of differential equations, Vol. 309 (February 2022) , p. 291-310, ISSN 1090-2732

DOI: 10.1016/j.jde.2021.11.035

20 p, 337.0 KB

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Articles > Research articles
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